Speaker: Jianing Yang

Abstract: The étale fundamental group of a scheme X describes the Galois étale covers of X. In characteristic 0, this is closely related to the topological fundamental groups for complex manifolds. However, in characteristic p, it can be much larger. Abhyankar’s conjecture classifies the finite Galois covers of affine curves in positive characteristic, i.e. the finite quotients of their fundamental groups. It was proven by Raynaud and Harbater in the 90s, using techniques like stable reduction of curves as well as formal and rigid patching.